Source: wikibot/behnke-stein-theorem-on-stein-manifolds

= Behnke–Stein theorem on Stein manifolds
{wiki=Behnke–Stein_theorem_on_Stein_manifolds}

The Behnke-Stein theorem is an important result in the theory of several complex variables, specifically concerning Stein manifolds. A Stein manifold is a type of complex manifold that generalizes certain properties of affine varieties and has favorable properties for complex analysis. The Behnke-Stein theorem states that: - A Stein manifold is holomorphically convex. This means that the set of holomorphic functions defined on the manifold can be used to separate points and provide control over compact sets.